Vibratory finishing process

Claim 2

In a workpiece having at least one exterior surface, the improvements comprising said exterior surface having a predefined desired average surface roughness (Ar) obtained by subjecting said exterior surface to a vibratory finishing process for a predetermined processing time (T opt ) defined as: ##EQU11## where T represents a time constant of the vibratory finishing system indicating the degree of response time of the system, Ir represents an initial average surface roughness of said exterior surface before exposure to the vibratory finishing process, and Dr represents a minimum average surface roughness for said exterior surface obtainable using the vibratory finishing process.

Claim 3

The workpiece as set forth in claim 1 wherein the workpiece is constructed from a steel material.

Claim 4

The workpiece as set forth in claim 1 wherein the initial roughness Ir of said exterior surface is derived by mechanical machining.

Claim 5

The workpiece as set forth in claim 1 wherein said exterior surface has a substantially cylindrical shape.

Claim 6

The workpiece as set forth in claim 4 wherein the diameter of said exterior surface effectively is reduced during the vibratory finishing process based upon a total stock removal S(t) defined as: S(t)=(m·t)+(2×4(Ir-Dr)(1-e.sup.-t/T)) where m represents a constant stock removal rate in diameter after the minimum average surface roughness Dr is obtained, and t represents a processing time for the vibratory finishing process.

Claim 7

The workpiece as set forth in claim 4 wherein the radius of said exterior surface effectively is reduced during the vibratory finishing process based upon a total stock removal S(t) defined as: S(t)=(m'·t)+4(Ir-Dr)(1-e.sup.-t/T) where m' represents a constant stock removal rate in the radius of said exterior surface after the minimum average surface roughness Dr is obtained, and t represents a processing time for the vibratory finishing process.

Claim 8

The workpiece as set forth in claim 1 wherein said exterior surface has a substantially noncylindrical shape.

Claim 9

The workpiece as set forth in claim 7 wherein the thickness of said exterior surface effectively is reduced during the vibratory finishing process based upon a total stock removal S(t) defined as: S(t)=(m'·t)+4(Ir-Dr)(1-e.sup.-t/T) where m' represents a constant stock removal rate in the thickness from said exterior surface of the noncylindrical workpiece after the minimum average surface roughness Dr is obtained, and t represents a processing time for the vibratory finishing process.

Claim 10

The workpiece as set forth in claim 1 wherein an arithmetic average surface roughness for said exterior surface at any particular processing time t during the vibratory finishing process (Ra(t)) is defined as: Ra(t)=(Ir-Dr)·e.sup.-t/T +Dr.

Claim 11

A workpiece, comprising: a first component having at least one working surface; a second component having at least one working surface, said working surface of said second component contacting the first component at the working surface during movement of said second component with respect to said first component; said working surfaces of said first component having a predefined desired average surface roughness (Ar 1 ) obtained by subjecting said first component to a conventional vibratory finishing process for a first predetermined processing time (T opt1 ), and said second component having a predefined desired average surface roughness (Ar 2 ) obtained by subjecting said second component to the vibratory finishing process for a second predetermined processing time (T opt2 ) wherein the predetermined processing time (T opt1 ) for said first component is defined as: ##EQU12## where T 1 , represents a time constant of the vibratory finishing system indicating the degree of response time of the system, Ir 1 , represents an initial average surface roughness of said first component, and Dr 1 , represents a minimum average surface roughness for said first component obtainable using the vibratory finishing process.

Claim 12

A workpiece, comprising: a first component having at least one working surface; a second component having at least one working surface, said working surface of said second component contacting the first component at the working surface during movement of said second component with respect to said first component; said working surfaces of said first component having a predefined desired average surface roughness (Ar 1 ) obtained by subjecting said first component to a conventional vibratory finishing process for a first predetermined processing time (T opt1 ), and said second component having a predefined desired average surface roughness (Ar 2 ) obtained by subjecting said second component to the vibratory finishing process for a second predetermined processing time (T opt2 ) wherein the predetermined processing time (T opt1 ) for said first component is defined as: ##EQU12## where T 1 , represents a time constant of the vibratory finishing system indicating the degree of response time of the system, Ir 1 , represents an initial average surface roughness of said first component, and Dr 1 , represents a minimum average surface roughness for said first component obtainable using the vibratory finishing process.

Claim 13

The workpiece as set forth in claim 10 wherein the predetermined processing time (T opt2 ) for said first component is defined as: ##EQU13## where T 2 , represents a time constant of the vibratory finishing system indicating the degree of response time of the system, Ir 2 represents an initial average surface roughness of said second component, and Dr 2 represents a minimum average surface roughness for said second component obtainable using the vibratory finishing process.

Claim 14

The workpiece as set forth in claim 10 wherein the workpiece is constructed from a steel material.

Claim 15

The workpiece as set forth in claim 10 wherein the profiles for the working surfaces of said first and second components are derived by mechanical machining.

Claim 16

The workpiece as set forth in claim 10 wherein said first component has a substantially cylindrical shape.

Claim 17

The workpiece as set forth in claim 14 wherein the diameter of said first component effectively is reduced during the vibratory finishing process based upon a total stock removal S(t) defined as: S(t)=(m·t)+(2×4(Ir.sub.1 -Dr)(1-e.sup.-t/T)) where m represents a constant stock removal rate in diameter after the minimum average surface roughness Dr is obtained, and t represents a processing time for the vibratory finishing process.

Claim 18

The workpiece as set forth in claim 10 wherein an arithmetic average surface roughness for said first component at any particular processing time t during the vibratory finishing process (Ra(t)) is defined as: Ra(t)=(Ir.sub.1 -Dr.sub.1)·e.sup.-t/T +Dr.sub.1.

Claim 19

A steel workpiece, comprising: at least one exterior surface having an initial average surface roughness (Ir) and profiles derived by mechanical machining which leaves said exterior surface with irregularities having directional orientation; said exterior surface having a desired average surface roughness (Ar) obtained by for a predetermined period of time (T opt ) based upon the initial average surface roughness (Ir), the desired average surface roughness (Ar) and a minimum average surface roughness obtainable for the workpiece (Dr) wherein the predetermined period of time (T opt ) is: ##EQU14## where T represents a time constant of the vibratory finishing system indicating the degree of response time of the system.

Claim 20

A steel workpiece, comprising: at least one exterior surface having an initial average surface roughness (Ir) and profiles derived by mechanical machining which leaves said exterior surface with irregularities having directional orientation; said exterior surface having a desired average surface roughness (Ar) obtained by for a predetermined period of time (T opt ) based upon the initial average surface roughness (Ir), the desired average surface roughness (Ar) and a minimum average surface roughness obtainable for the workpiece (Dr) wherein the predetermined period of time (T opt ) is: ##EQU14## where T represents a time constant of the vibratory finishing system indicating the degree of response time of the system.

Claim 21

A vibratory finishing process for producing a predefined desired average surface roughness (Ar) on an exterior surface of a workpiece in a minimum processing time (T opt ), comprising the steps of: mechanically machining the exterior surface of the workpiece, whereby the exterior surface has an initial average surface roughness (Ir); inserting the workpiece in a tub along with a plurality of abrading elements; and vibrating the tub for the predetermined time interval (T opt ) to obtain the desired average surface roughness (Ar) on the exterior surface of the workpiece by moving the abrading elements into contact with the exterior surface wherein the step of vibrating the tub for the predetermined time interval (T opt ) includes vibrating the tub for the time interval defined as: ##EQU15## where T represents a time constant of the vibratory finishing system indicating the degree of response time of the vibratory finishing process, and Dr represents a minimum average surface roughness obtainable for the exterior surface.

Claim 22

A vibratory finishing process for producing a predefined desired average surface roughness (Ar) on an exterior surface of a workpiece in a minimum processing time (T opt ), comprising the steps of: mechanically machining the exterior surface of the workpiece, whereby the exterior surface has an initial average surface roughness (Ir); inserting the workpiece in a tub along with a plurality of abrading elements; and vibrating the tub for the predetermined time interval (T opt ) to obtain the desired average surface roughness (Ar) on the exterior surface of the workpiece by moving the abrading elements into contact with the exterior surface wherein the step of vibrating the tub for the predetermined time interval (T opt ) includes vibrating the tub for the time interval defined as: ##EQU15## where T represents a time constant of the vibratory finishing system indicating the degree of response time of the vibratory finishing process, and Dr represents a minimum average surface roughness obtainable for the exterior surface.

Claim 23

The vibratory finishing process as set forth in claim 18 wherein said exterior surface has a substantially cylindrical shape.

Claim 24

The vibratory finishing process as set forth in claim 19 further including the step of effectively reducing the diameter of the exterior surface effectively as the tub is vibrated to obtain a total stock removal S(t) of: S(t)=(m·t)+(2×4(Ir-Dr)(1-e.sup.-t/T)) where m represents a constant stock removal rate in diameter after the minimum average surface roughness Dr is obtained, and t represents a processing time for the vibratory finishing process.